Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#376 ⋊ C2 |
| Sylow | C3 ⋊ #1963 |
320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(4,5,6,7)(10,18)(14,22)(17,23)(19,20);(8,10)(9,14,16,22)(11,19)(12,20)(13,18)(15,17,21,23);(2,3)(5,7)(8,9,12,15,13,16,11,21)(10,17,20,22,18,23,19,14)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,c^b=cg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10681962, #10687539, #10687544, … |
| maximal normal subgroup of | #10681962, #10687539, #10687544, … |
| maximal quotient of | #10693973, #10693977, #10693981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2016);